Linear induction motor (LIM)

Reference notes

A linear induction motor (LIM) is a rotary induction motor unrolled into a flat plane. The stator becomes a straight rail of laminated iron with 3-φ windings; the rotor becomes a flat conducting sheet that slides along the rail. Use Next → to walk through the construction variants, slip / thrust equations, the end-effect efficiency penalty unique to linear topology, maglev applications, and contrast with the linear synchronous motor (LSM).

How it works

• 3-φ stator currents create a magnetic field that travels along the rail (instead of rotating) at synchronous linear speed v_s.
• Traveling field induces currents in the conducting sheet → currents experience J × B force → thrust pushes the sheet along.
• Same physics as rotary IM; linear analog of every quantity (v ↔ ω, F ↔ T, etc.).

where τ is the pole pitch (distance between adjacent N and S poles, typically 10–30 cm) and f is the supply frequency.

Construction variants

• Short-stator — moving stator (few-meter active winding) traveling along a long passive reaction rail. Vehicle carries the active windings and power cables. Used in urban transit (SkyTrain, KL LRT).
• Long-stator — long fixed stator (kilometers of guideway), short passive rotor on the vehicle. Stator sections energized as vehicle passes via section breakers. Used in Transrapid maglev.
• Single-sided — stator on one side only. Simpler, but produces asymmetric normal force pulling rotor toward stator.
• Double-sided — two stators sandwich the reaction sheet. Normal forces balance; double iron mass.

Slip and thrust

Same form as rotary induction motor torque equation, with thrust replacing torque and linear velocity replacing angular. Power P = F · v.

Maximum thrust at s_max = R₂' / X — typically 20–40 % slip, much higher than the few-percent slip of rotary IMs. LIMs typically run at 5–30 % slip to balance thrust and efficiency.

End effects — the LIM efficiency penalty

Because the stator is finite in the direction of motion (unlike a rotary IM where the magnetic loop is closed):

• Entry edge — rotor material enters cold (no eddy currents). Time-changing flux induces a startup transient → drag force.
• Exit edge — rotor leaves carrying residual eddy currents that decay over a short distance → additional thrust loss.

Result: LIM efficiency 60–80 %, vs 85–95 % for rotary IM. Mitigations: long pole pitch, end-compensation windings, graded magnetic shielding.

Maglev applications

• Transrapid (Germany, Shanghai) — long-stator LIM in guideway, separate electromagnetic levitation. 430 km/h commercial service since 2004.
• JR-Maglev (Japan) — superconducting LIM with onboard cryogenic magnets and figure-of-eight ground coils. 603 km/h record. Chuo Shinkansen Tokyo-Nagoya line under construction.
• Both eliminate wheel-rail friction → enable speeds > 400 km/h.

Urban transit (LIM-driven wheel-on-rail, no maglev)

Many systems use LIM only for propulsion with conventional wheels and rails. Advantages: no traction motors on bogies, robust passive aluminum reaction rail in track center, tolerates steep gradients (no friction-limited traction), quiet operation. Examples:

• Vancouver SkyTrain (since 1986).
• Toronto Scarborough RT (1985–2023).
• Detroit People Mover (1987).
• Kuala Lumpur LRT (1996).
• Beijing Capital Airport Line (2008).
• Vancouver Canada Line (2009).

EMALS — naval aircraft catapult

Ford-class US Navy carriers replaced steam catapults with the Electromagnetic Aircraft Launch System: a long-stator LIM along a 100-meter trough accelerates an aircraft from 0 to ~240 km/h in ~2 seconds (~12 g horizontal). Advantages over steam: precise energy control per aircraft, lower thermal stress, faster cycle, smaller plant footprint.

Other industrial uses

• Roller-coaster launches — accelerate cars to 100+ km/h in seconds; replaces older counterweight catapults.
• Electromagnetic pumps for liquid sodium — fast nuclear reactors; no mechanical seals.
• Semiconductor fab handling — magnetic levitation conveyors for contactless wafer transport.

LIM vs LSM (Linear Synchronous Motor)

Tubular LIM

Windings wrapped circumferentially around a cylindrical rod create a tubular LIM — compact linear actuators for industrial automation.